The proof of this inequality follows [1]}, [2]}. Hence, the surrogate function that majorizes \(\sigma (\mathbf {P}^e)\)  is as follows:
\(\tau (\mathbf {P}^e, \mathbf {Y}) = \operatorname{Tr}{\mathbf {P}^e}^T \mathbf {V} \mathbf {P}^e + k - 2~\operatorname{Tr}{\mathbf {P}^e}^T \mathbf {B}(\mathbf {Y}) \mathbf {Y}.\) 
